# Luboš Motl

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bio website motls.blogspot.com location Czech Republic age 40 member for 2 years, 10 months seen 22 hours ago profile views 2,400

Hi, I am a string theorist and a publicist.

# 259 Actions

 Jul9 answered Closed-form Expression for $\sum_{j=0}^{k-1}(2j+2)\sum_{i=1}^j \frac 1 {i^2}$? (problem with Mathematica) Jul9 answered Compositions of prime numbers Jun27 comment Validity of $\sum_{i=1}^n(a_i^2+b_i^2+c_i^2+d_i^2)\lambda_i\geq\lambda_1+\lambda_2+\lambda_3+\lambda_4$? Oh, I see, you're right. Jun27 comment Puzzle: $(\Box @)+(\Box @) = (\Box\bigstar\Box$) Thanks for your care and implicit compliments, @JTL and @Jyrki, but I don't think it's a big issue. Let's be generous, people have the right to vote the way they want. Jun27 awarded Nice Answer Jun26 revised Validity of $\sum_{i=1}^n(a_i^2+b_i^2+c_i^2+d_i^2)\lambda_i\geq\lambda_1+\lambda_2+\lambda_3+\lambda_4$? added 99 characters in body; added 570 characters in body; added 2 characters in body Jun26 revised Puzzle: $(\Box @)+(\Box @) = (\Box\bigstar\Box$) added 123 characters in body Jun26 revised Validity of $\sum_{i=1}^n(a_i^2+b_i^2+c_i^2+d_i^2)\lambda_i\geq\lambda_1+\lambda_2+\lambda_3+\lambda_4$? added 454 characters in body; added 39 characters in body; added 55 characters in body; added 47 characters in body Jun26 comment Validity of $\sum_{i=1}^n(a_i^2+b_i^2+c_i^2+d_i^2)\lambda_i\geq\lambda_1+\lambda_2+\lambda_3+\lambda_4$? Interesting, I jumped on the same intuition as you did - it couldn't be right, I thought, because the RHS didn't have the minimal $\lambda$ anymore. Of course, the catch is that the "generalization" has almost nothing to do with the original inequality. Jun26 answered Validity of $\sum_{i=1}^n(a_i^2+b_i^2+c_i^2+d_i^2)\lambda_i\geq\lambda_1+\lambda_2+\lambda_3+\lambda_4$? Jun26 comment How to take the inverse of this signal? You were faster, I erased my answer. ;-) Jun26 answered Puzzle: $(\Box @)+(\Box @) = (\Box\bigstar\Box$) Jun26 answered Eigenvectors of a normal matrix Jun26 answered How common is the use of the term “primitive” to mean “antiderivative”? Jun26 comment Plane intersecting line segment The objects you called $dist$ are not distances in the exact sense. They're inner products which can be both positive and negative. There's no reason to divide the debate to the positive and negative case because all the geometrically natural formulae here are linear, rational, or otherwise analytic and they work uniformly both for positive and negative values of the inner products. Jun26 comment Plane intersecting line segment Dear @PUK, if a line belongs to a plane, then it surely is parallel with it. At any rate, when it is so, the intersection - as in set theory - of the plane and the line is the whole line (the very same one). I don't understand in what sense it would make sense to pick two particular points on the line as "better intersections" than all the other points. Also, I am confused by your separate discussion of negative and positive values of $dist.dist$. A fun about maths and algebra is that one may calculate with negative numbers just like with the positive ones w/o splitting derivations. Jun25 revised Plane intersecting line segment added 66 characters in body Jun25 revised Plane intersecting line segment added 32 characters in body Jun25 answered Plane intersecting line segment Jun18 answered How to partial differential of a trace of matrix form?